Strategy of statistical model selection for precision farming on-farm experiments

Nitrogen (N) fertilization implies two important issues: N enhances grain yields and quality, but applied in excess, nitrous oxide emissions and nitrate leaching may be induced. To reduce environmental impacts, spatial N variability in agricultural fields can be adapted using crop sensors. In on-farm experiments, sensor-based variable rate N application is compared to uniform N application, which is common agricultural practice. On-farm experiments (OFE) provide special considerations as opposed to on-station trials. In OFE, the experimental units in farmer-managed fields are considerably larger, which raises the question if soil heterogeneity may be fully controlled by the experimental design (random treatment allocation and blocking). Grain yield monitoring systems are used increasingly in OFE and provide spatially correlated data. As a consequence, classical analysis of variance is not a valid option. An alternative four-step strategy of statistical model selection is presented, generalizing the assumptions of classical analysis of variance within the framework of linear mixed models. Soil heterogeneity is preliminary identified in step 1 and finalized in step 2 using covariate combinations (analysis of covariance). Yield data correlations are handled in step 3 using geo-statistical models. The last step estimates treatment effects and derives the statistical inference. Analyses of three OFE revealed that different covariate combinations and geo-statistical models were needed for each trial, which involves higher analytical efforts than for on-station trials. These efforts can be minimized by following the steps provided in this study to find a best model approximation. Nevertheless, model selection in precision farming OFE will always accompany some uncertainty.